Invariants
Base field: | $\F_{139}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 22 x + 139 x^{2} )( 1 - 21 x + 139 x^{2} )$ |
$1 - 43 x + 740 x^{2} - 5977 x^{3} + 19321 x^{4}$ | |
Frobenius angles: | $\pm0.117174211439$, $\pm0.150285916016$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $0$ |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $14042$ | $366243444$ | $7207243370936$ | $139356758471807520$ | $2692475295239121032102$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $97$ | $18953$ | $2683642$ | $373309321$ | $51889289707$ | $7212557728946$ | $1002544484403433$ | $139353668544736081$ | $19370159755029946318$ | $2692452204285043607753$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{139}$.
Endomorphism algebra over $\F_{139}$The isogeny class factors as 1.139.aw $\times$ 1.139.av and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
Twist | Extension degree | Common base change |
---|---|---|
2.139.ab_ahc | $2$ | (not in LMFDB) |
2.139.b_ahc | $2$ | (not in LMFDB) |
2.139.br_bcm | $2$ | (not in LMFDB) |